Degradation Data Analysis Using Wiener Processes With Measurement Errors

A novel Wiener process model with measurement errors for degradation analysis

“…For clear, let M 0 denote the proposed model. The Wiener process with measurement errors in [20] is considered as a reference method M 1 for comparison. To settle the linear degradation path problem, we assume the transformed time scale to be ( ) t a bt Λ = + , and let β µκ , N 2 ( ) be a normally distributed random effect.…”

“…Without loss of generality in simulation, degradation data are first simulated based on the proposed model, and then the model presented in [20] and our model are adopted to fit the simulated degradation. Based on simulation studies, we found that if the degradation model of Equation (10) is utilized to generate the degradation data, not all simulated deterioration processes can be properly depicted by [20] because the limitation between mean and variance functions. To illustrate this important issue, we give two examples here.…”

“…Although they ignored the autocorrelation in their study, more and more deterioration models have taken this issue into consideration in the model construction procedure. Among these models, the Wiener process with positive drift is a favourable candidate due to its mathematical properties and physical interpretations [20]. The sciENcE aNd tEchNology regular Wiener process η( ), t t ≥ { } 0 with drift β and diffusion σ can be expressed as the well-adopted form [16,18] There has been considerable interest on the part of the scientists and engineers in applying this process in degradation reliability analysis.…”

“…Motivated by laser data [7], Peng and Tseng [11] proposed a generalized formulation of the linear degradation path in which the unit-to-unit variation, the time-dependent error structure and the measurement error were considered simultaneously. To utilize the first inspection of each unit, Ye et al [20] improved the model in [18] We call this proposed Wiener process model with measurement errors expressed by Equation (4) the simple model. And we will illustrate it in Section 2.…”

“…Section 3 takes measurement errors into the simple model and gives the model description, MLE for unknown parameter and initial guesses for optimization algorithm. In Section 4, the efficiency and reasonability of our methodology is validated comparing with the Wiener processes with measurement errors in [20] via a Monte Carlo simulation study. In Section 5, the proposed approach is illustrated by two applications including storage disks degradation analysis and Infrared light-emitting diodes (IRLEDs) degradation analysis, and comparative results are given.…”